$1/\varphi$ Spectrum of the Stress Dynamics with the Bak-Tang-Wiesenfeld Sandpile

TL;DR

This paper reveals a $1/\varphi$ noise spectrum in the stress dynamics of the BTW sandpile, linking it to self-organized criticality and stress-release cycles, providing insights into the underlying mechanisms of SOC.

Contribution

It demonstrates the presence of a $1/\varphi$ spectrum in the BTW sandpile's stress dynamics, connecting noise characteristics to SOC mechanisms.

Findings

$1/\varphi$ noise observed in stress dynamics.

Stress cycles involve gradual accumulation and abrupt release.

Spectrum extends infinitely in the thermodynamic limit.

Abstract

With the original Bak-Tang-Wisenefeld (BTW) sandpile we uncover the $1/\varphi$ noise in the mechanism maintaining self-organized criticality (SOC) - the question raised together with the concept of SOC. We posit that the dynamics of stress in the BTW sandpile follows quasi-cycles of graduate stress accumulation that end up with an abrupt stress-release and the drop of the system to subcritical state. In thermodynamic limit, the intra-cycle dynamics exhibits the $1/\varphi$ spectrum that extends infinitely and corresponds to the stress-release within the critical state.